My current project emphasizes a high skill ceiling and tactical complexity. It contains some FPS elements that are (intentionally) difficult to master, and while I consider myself a decent FPS player, some high level strategies are beyond my ability to execute reliably. We've found a few ways to test competitive gameplay anyway:
AI can make a good practice partner
The most valuable tool in understanding and finetuning our game was to play with and against AI opponents with near-perfect aim and timing. Not only did it allow us to test strategies that we weren't skilled enough to execute, trying your best to beat an "infallible" opponent can lead to all sorts of insights and creative strategies.
Of course, the viability of "super-skilled" AI depends heavily on the type of game you're making, but for the purposes of balance testing, it doesn't need to be perfect, all-encompassing or fair. Don't be afraid to leave some "holes" in their abilities or have them cheat if you know what the outcome of a good move should look like.
Condense your tests
Sometimes you can only get a good feel for a mechanic if you experience it. For example, landing a complicated combo in a fighting game via the intended means plays rather differently from triggering it with a single button press, so cheating won't give you the required data. What you can do, however, is get yourself as close to the situation as possible.
If you know what aspect you want to test, set up that specific scenario and a trigger to reset game state quickly and painlessly, then play through that until you grok the play, even if you can't replicate it reliably. In the fighting game example, place your character right next to an opponent, set your combo bar to full and have at it. It doesn't matter if you mess up the combo 90% of the time, nailing it just a few times is a useful experience.
Go crazy once in a while
A good way to get a better feel for your game is to tweak the core mechanics in silly ways now and then. Set the global damage multiplier to 1000%, or to 10%. Adjust the game speed, gravity, amount of resources, unit costs, weapon ranges, whatever will break the game in interesting ways. Try to exploit the changes and see which niche strategies might work in the "proper" game as well, and how to counter them.
Good mechanics are somewhat self-balancing
A core aspect of good game balance is setting up mechanics that counteract any one element or strategy that turns out a smidge too powerful. Whether it's by providing viable counter-picks for any option (LoL), items that alter the core game rules (MtG) or just a general system of soft counters (Starcraft), aim for a system that seeks equilibrium. It might not come to rest exactly where you predicted, but it should stabilize somewhere.
Follow similar games
Few developers have the luxury of a sufficiantly large and dedicated audience to really push the limits of competitive play. If you happen to work on Starcraft or League of Legends - congratulations, but why are you reading this? If you don't, consider picking a successful game or two that's similar to your project in some regard and following the meta, professional matches and analyses for a while. You'll pick up a lot of genre theory that might help you avoid common pitfalls or serve as a tool to examine your own project in a new light.